KAMPHOT and the Effect of Dead Pixels

Completely dead or unresponsive pixels can have a deleterious effect on the data if not accounted for correctly. Depending on the exact definition, 0.2-1.0% of the pixels in a NICMOS array may be considered as dead. These pixels will affect a surprising fraction of all sources since each source is seen 6 times and illuminates 1-4 pixels in each frame depending on the seeing. The fraction of affected sources could be as large as 10-20%.

Dead pixels can do more than increase the measurement dispersion, they can result in a significant measurement bias as well. Consider two ways of treating the measurements:

 
Figure 6:   a) A schematic representation of the camera data (upper left) for 3 separate frames of data, the bad pixel mask (lower left) (1=good,-1=bad), the resampled data (upper right), the surface brightness computed for the 2 processing algorithms, and the amplitude calculated from the data. When there are no bad pixels both algorithms determine the surface brightness and total source amplitude correctly. b) The lower panel repeats the upper one, but with one bad pixel. Energy is lost that results in an incorrect estimate of the surface brightness unless bad pixels are taken into account.

• In the simple coadd process, one resamples the data and ignores a bad pixel in computing the average surface brightness in the final output image. Unfortunately, for undersampled data the average surface brightness will be computed incorrectly as suggested by the cartoon in Figure 6. If there are NSAMP measurements of a source, and if a source spreads its energy over 2 pixels in each frame, then the amplitude error could be as large as for NSAMP=6 if the missing energy is not properly accounted for.

• IPAC's KAMPHOT algorithm was designed to take advantage of the knowledge that a dead pixel was involved in one, or more, of the measurements. In the simplest terms, KAMPHOT throws out the entire frame containing a bad pixel so that the average brightness is not contaminated by incomplete data from a bad frame. As actually implemented, KAMPHOT uses the partial information in even a corrupted as part of its fitting procedure. The cartoon in Figure 6 shows that rejecting the bad frame leads to an accurate measurement of the source amplitude whereas the simple coadd scheme makes a 17% error in the NSAMP=3 case.

The Monte Carlo simulation of this process adopts the procedure described in the preceding section but randomly makes % of the pixels dead. The data are summed taking dead pixels into account using either of the 2 algorithms described above. Figure 7 shows the amplitude bias as a function of the seeing for the coadd and KAMPHOT algorithms. A bias of 2-5% will affect 10% of the sources if the full information about dead pixels is not taken into account (Figure 7). Figure 8 shows the distribution of source amplitudes for a particular case (2 seeing, 0.2 dead perimeter, 1% dead pixels) for the 2 measurement techniques. A long non-Gaussian tail along with a significant bias are apparent for the coadd photometry, but are absent for the KAMPHOT photometry.

 
Figure 7:   The amplitude bias as a function of seeing for the coadd and KAMPHOT algorithms.

The uncertainty of the KAMPHOT photometry for a source contaminated with a bad pixel will be larger compared with that for a perfect source. The effect might be even smaller than this, since KAMPHOT makes use of the partial information available in a bad frame.

The robustness of KAMPHOT against the effects of dead pixels suggests that it will not be necessary to purchase science-grade arrays of extra high quality. So long as the dead pixel number does not exceed %, it should be possible to obtain accurate photometry.

 
Figure 8:   Histograms of source amplitudes for the coadd and KAMPHOT algorithms show that simple photometry from the coadds incorrectly accounts for the presence of bad pixels.